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NCERT Solutions for Exercise 6.2 Class 10 Maths Chapter 6 Triangles are discussed here. These NCERT solutions are created by subject matter expert at Careers360 considering the latest syllabus and pattern of CBSE 2023-24. Class 10 maths ex 6.2 contains two theorems: (Theorem 1) When a parallel line is drawn along one of the triangle's sides and intersects the other two sides at certain points, the two sides are divided in the same proportion. (Theorem 2) Any line that divides the two sides of a triangle in the same ratio is parallel to the third side.
NCERT solutions for exercise 6.2 Class 10 Maths chapter 6 Triangles discusses about the concept triangle as a polygon, interior angles of a triangle, exterior angles of triangle, Pythagoras' theorem, and conditions of similarity in triangles. 10th class Maths exercise 6.2 answers are designed as per the students demand covering comprehensive, step by step solutions of every problem. Practice these questions and answers to command the concepts, boost confidence and in depth understanding of concepts. Students can find all exercise together using the link provided below.
Triangles Class 10 Chapter 6 Exercise: 6.2
Q1 In Fig. 6.17, (i) and (ii), DE || BC. Find EC in (i) and AD in (ii).
Answer:
(i)
Let EC be x
Given: DE || BC
By using the proportionality theorem, we get
(ii)
Let AD be x
Given: DE || BC
By using the proportionality theorem, we get
Answer:
(i)
Given :
PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm
and
We have
Hence, EF is not parallel to QR.
Answer:
(ii)
Given :
PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm
and
We have
Hence, EF is parallel to QR.
Q2 (3) E and F are points on the sides PQ and PR respectively of a triangle PQR. For each of the following cases, state whether EF || QR : PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.36 cm
Answer:
(iii)
Given :
PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.36 cm
and
We have
Hence, EF is parallel to QR.
Q3 In Fig. 6.18, if LM || CB and LN || CD, prove that
Answer:
Given : LM || CB and LN || CD
To prove :
Since , LM || CB so we have
Also, LN || CD
From equation 1 and 2, we have
Hence proved.
Q4 In Fig. 6.19, DE || AC and DF || AE. Prove that BF / FE = BE / EC
Answer:
Given : DE || AC and DF || AE.
To prove :
Since , DE || AC so we have
Also,DF || AE
From equation 1 and 2, we have
Hence proved.
Q5 In Fig. 6.20, DE || OQ and DF || OR. Show that EF || QR.
Answer:
Given : DE || OQ and DF || OR.
To prove EF || QR.
Since DE || OQ so we have
Also, DF || OR
From equation 1 and 2, we have
Thus, EF || QR. (converse of basic proportionality theorem)
Hence proved.
Answer:
Given : AB || PQ and AC || PR
To prove: BC || QR
Since, AB || PQ so we have
Also, AC || PR
From equation 1 and 2, we have
Therefore, BC || QR. (converse basic proportionality theorem)
Hence proved.
Answer:
Let PQ is a line passing through the midpoint of line AB and parallel to line BC intersecting line AC at point Q.
i.e. and .
Using basic proportionality theorem, we have
Since
Q is the midpoint of AC.
Answer:
Let P is the midpoint of line AB and Q is the midpoint of line AC.
PQ is the line joining midpoints P and Q of line AB and AC, respectively.
i.e. and .
we have,
From equation 1 and 2, we get
By basic proportionality theorem, we have
Answer:
Draw a line EF passing through point O such that
To prove :
In , we have
So, by using basic proportionality theorem,
In , we have
So, by using basic proportionality theorem,
Using equation 1 and 2, we get
Hence proved.
Answer:
Draw a line EF passing through point O such that
Given :
In , we have
So, by using basic proportionality theorem,
However, its is given that
Using equation 1 and 2 , we get
(By basic proportionality theorem)
Therefore, ABCD is a trapezium.
NCERT solutions Class 10 Maths chapter 6 exercise 6.2 triangles necessitates a thorough understanding of the underlying theorems. As a result, students are advised to read through the logical explanations of the theorems' proofs, as well as practise them using well-explained diagrams.
NCERT solutions Class 10 Maths chapter 6 exercise 6.2 may be mastered if students remember and comprehend how the theorems are applied. Children should consider creating a theory chart that they can refer to from time to time. Another creative and simple way to comprehend theorems is to use everyday objects. Students might ask their teachers and parents for assistance in doing the same. Students can also access Triangles Class 10 Notes here and use them for quickly revision of the concepts related to Triangles.
Also see-
The term "similar" refers to two figures that have the same shape but differ in size.
The figures that are congruent are all similar, but the opposite is not true.
If we know the side ratio and the length of the any side, we can find the length of the corresponding side of the other triangle by using the ratio.
The ration of area of the triangles is equal to the square of the ratio of the sides.
The ration of area of the triangles is equal to the square of the ratio of the sides.
Ratio of area = 1:4
4/x=1/3
x=12cm
The length of the longer side is 12cm.
It will always be parallel to the third side of the triangle.
No, resemblance only relates to the shape of the figures and does not imply equality.
Exam Date:01 January,2025 - 14 February,2025
Exam Date:01 January,2025 - 14 February,2025
Hello
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Hello Aspirant, Hope your doing great, your question was incomplete and regarding what exam your asking.
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